Abstract
Linear models with two variance components are considered and a new class of nonnegative estimators for singular variance component is presented. It is proved that this class consists of admissible nonnegative invariant quadratic estimators with respect to the mean squared loss function. Numerical results of the mean squared errors of the proposed estimators for one-way ANOVA model are reported.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Gnot, S. and Kleffe, J. (1983). Quadratic estimation in mixed linear models with two variance components. Journal of Statistical Planning and Inference 8 267–279.
Gnot, S., Kleffe, J. and Zmyslony, R. (1985). Nonnegativity of admissible invariant quadratic estimates in mixed linear models with two variance components. Journal of Statistical Planning and Inference 12 249–258.
Gnot, S., Trenkler, G. and Zmyslony, R. (1993). Nonnegative estimation of the weighted squared lenght of the parameter vector in the linear regression model. Submitted for publication.
Hartung, J. (1981). Nonnegative minimum biased invariant estimation in variance component models. The Annals of Statistics 9, 278–292.
Kleffe, J. and Pincus R. (1974). Bayes and best quadratic unbiased estimators for variance components and heteroscedastic variances in linear model. Mathematische Operationsforschung und Statistik, Series Statistics 5 147–159.
Mathew, T., Sinha, B. K. and Sutradhar, B. C. (1992). Nonnegative estimation of variance components in unbalanced mixed models with two variance components. Journal of Multivariate Analysis 42 77–101.
Olsen, A., Seely, J. and Birkes, D. (1976). Invariant quadratic unbiased estimation for two variance components. The Annals of Statistics 4 878–890.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1994 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Gnot, S., Trenkler, G., Stemann, D. (1994). Admissible Nonnegative Invariant Quadratic Estimation in Linear Models with Two Variance Components. In: Caliński, T., Kala, R. (eds) Proceedings of the International Conference on Linear Statistical Inference LINSTAT ’93. Mathematics and Its Applications, vol 306. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-1004-4_15
Download citation
DOI: https://doi.org/10.1007/978-94-011-1004-4_15
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-4436-3
Online ISBN: 978-94-011-1004-4
eBook Packages: Springer Book Archive